Conundrum

Co`nun´drum

n.	1.	A kind of riddle based upon some fanciful or fantastic resemblance between things quite unlike; a puzzling question, of which the answer is or involves a pun. Or pun ambiguous, or conundrum quaint. - J. Philips.
	2.	A question to which only a conjectural answer can be made. Do you think life is long enough to let me speculate on conundrums like that? - W. Black.

Noun

conundrum - a difficult problem

Synonyms: brain-teaser, riddle, enigma